Thursday, March 14, 2013

It can seem a bit ironic that we should be discussing Nassim Taleb's best-seller "Antifragile" here, since most algorithmic trading strategies involve predictions and won't be met with approval from Taleb. Predictions, as Taleb would say, are "fragile" -- they are prone to various biases (e.g. data snooping bias) and the occasional Black Swan event will wipe out the small cumulative profits from many correct bets. Nevertheless, underneath the heap of diatribes against various luminaries ranging from Robert Merton to Paul Krugman, we can find a few gems. Let me start from the obvious to the subtle:

1) Momentum strategies are more antifragile than mean-reversion strategies.

Taleb didn't say that, but that's the first thought that came to my mind. As I argued in many places, mean reverting strategies have natural profit caps (exit when price has reverted to mean) but no natural stop losses (we should buy more of something if it gets cheaper), so it is very much subject to left tail risk, but cannot take advantage of the unexpected good fortune of the right tail. Very fragile indeed! On the contrary, momentum strategies have natural stop losses (exit when momentum reverses) and no natural profit caps (keep same position as long as momentum persists). Generally, very antifragile! Except: what if during a trading halt (due to the daily overnight gap, or circuit breakers), we can't exit a momentum position in time? Well, you can always buy an option to simulate a stop loss. Taleb would certainly approve of that.

2) High frequency strategies are more antifragile than low frequency strategies.

Taleb also didn't say that, and it has nothing to do with whether it is easier to predict short-term vs. long-term returns. Since HF strategies allow us to accumulate profits much faster than low frequency ones, we need not apply any leverage. So even when we are unlucky enough to be holding a position of the wrong sign when a Black Swan hits, the damage will be small compared to the cumulative profits. So while HF strategies do not exactly benefit from right tail risk, they are at least robust with respect to left tail risk.

3) Parameter estimation errors and vulnerability to them should be explicitly incorporated in a backtest performance measurement.

Suppose your trading model has a few parameters which you estimated/optimized using some historical data set. Based on these optimized parameters, you compute the Sharpe ratio of your model on this same data. No doubt this Sharpe ratio will be very good, due to the in-sample optimization. If you apply this model with those optimized the parameters on out-of-sample data, you would probably get a worse Sharpe ratio which is more predictive. But why stop at just two data sets? We can find N different data sets of the same size, calculate the optimized parameters on each of them, but compute the Sharpe ratios over the N-1 out-of-sample data sets. Finally, you can average over all these Sharpe ratios. If your trading model is fragile, you will find that this Sharpe ratio is quite low. But more important than Sharpe ratios, you should compute the maximum drawdown based on each set of parameters, and also the maximum of all these max drawdowns. If your trading model is fragile, this maximum of maximum drawdowns is likely to be quite scary.

The scheme I described above is called cross-validation and is well-known before Taleb, though his book reminds me of its importance.

4) Notwithstanding 3) above, a true estimate of the max drawdown is impossible because it depends on the estimate of the probability of rare events. As Taleb mentioned, even in case of a normal distribution, if the "true" standard deviation is higher than your estimate by a mere 5%, the probability of a 6-sigma event will be increased by 5 times over your estimate! So really the only way to ensure that our maximum drawdown will not exceed a certain limit is through Constant Proportion Portfolio Insurance: trading risky assets with Kelly-leverage in a limited liability company, putting money that you never want to lose in a FDIC-insured bank, with regular withdrawals from the LLC to the bank (but not the other way around).

5) Correlations are impossible to estimate/predict. The only thing we can do is to short at +1 and buy at -1.

Taleb hates Markowitz portfolio optimization, and one of the reasons is that it relies on estimates of covariances of asset returns. As he said, a pair of assets that may have -0.2 correlation over a long period can have +0.8 correlation over another long period. This is especially true in times of financial stress. I quite agree on this point: I believe that manually assigning correlations with values of +/-0.75, +/-0.5, +/-0.25, 0 to entries of the correlation matrix based on "intuition" (fundamental knowledge) can generate as good out-of-sample performance as any meticulously estimated numbers.The more fascinating question is whether there is indeed mean-reversion of correlations. And if so, what instruments can we use to profit from it? Perhaps this article will help.

6) Backtest can only be used to reject a strategy, not to predict its success.

This echoes the point made by commenter Michael Harris in a previous article. Since historical data will never be long enough to capture all the possible Black Swan events that can occur in the future, we can never know if a strategy will fail miserably. However, if a strategy already failed in a backtest, we can be pretty sure that it will fail again in the future.

===

The online "Quantitative Momentum Strategies” workshop that I mentioned in the previous article is now fully booked. Based on popular demand, I will offer a "Mean Reversion Strategies" workshop in May. Once again, it will be conducted in real-time through Skype, and the number of attendees will be similarly limited to 4. See here for more information.